1

Astronomical Systems

This table lists nearly a hundred astronomical systems from the Han period to the end of imperial China. It omits half a dozen early schemata (items 1-6 in CTK) that generate only simple lunisolar calendars, and about which little is known. Item 1 is a version of one of these, important because item 4, a complete system, was based on it, and item 2 was explicitly meant to reform it. On the "old" Warring States calendars see Chen 2003: 87-92.

This is far from a complete list. Of the roughly 200 systems of which there is some record, I include only those about which we have some basic information. Almost all occur in three sources, the Season-granting system (SGS); Ch’en Mei-tung 1995: 215-23, table 8-1 (CMT); and Ch’en Tsun-kuei 1980-84: III, 1399-1407, table 50 (CTK). I have also consulted Yabuuti 1963, which lists additional systems about which there is very little reliable information.

The Title column contains only those from SGS. Titles in the form "nth year" refer to the sexagenary year number of the epoch. The dynasty column uses the abbreviations F. (former, ch’ien 前), L. (latter, hou 後), N. (northern, pei 北), E. (eastern, tung 東), S. (southern, nan 南), and W. (western, hsi 西). In the last column, inclusive dates are those of official use as given in SGS. Single dates mark either systems that did not achieve official status or official systems not recognized by SGS. A number of the dates in SGS are incorrect; see my notes. Those in CTK are also often inexact. Many of the dates require further study; I have added in square brackets the terminal dates of official status when known. In the "dynasty" column I add a plus sign when a system remained official past the end of a dynasty. Although I normally list only the person customarily credited with authorship, most systems were the products of collaboration.

No.	SGS	CMT	CTK	Dynasty	Title	Title in CMT or CTK	Author	Dates
1		1		F. Han		Quarter-Day (Ssu fen li 四分暦)	Anonymous	Unknown
2		2	7	F. Han	Grand Inception (T’ai ch’u 太初)		Teng P’ing 鄧平	104 B.C-A.D.1/5
3	1		8	F. Han+	Triple Concordance (San t’ung li 三統暦)		[Liu Hsin 劉歆]	A.D. 1/5-85 (note 1)
4	2	3	9	L. Han	Quarter-Day (Ssu fen li 四分暦)	Later Han Quarter-Day ([Hou Han] Ssu fen li [後漢] 四分暦)	Pien Hsin 編訢	85-206
5	3	4	10	L. Han+	Supernal Emblem (Ch’ien hsiang li 乾象暦)		Liu Hung 劉洪	206-37
6		5	11	Wei		Yellow Inception (Huang ch’u li 黃初暦)	Han I 韓翊	220
7		6	12	Wei		Grand Harmony (T’ai ho li 太和暦)	Kao T’ang-lung 高堂隆	227
8	4	7	13	Wei+	Luminous Inception (Ching ch’u li 景初暦)		Yang Wei 楊偉	237-443
9			16	Tsin		Supernal Standard (Ch’ien tu li 乾度暦)	Li Hsiu 李修	c. 277
10		8	17	Tsin+		Perpetual Harmony (Yung ho li 永和暦)	Wang Shuo-chih 王朔之	352
11			15	Tsin		Correct (Cheng li 正暦)	Liu Chih劉智	c. 352
12		9	14, 20	Tsin		Grand Beginning (T’ai shih li 泰始暦)	Liu Chih	365
13		10	18	L. Ch’in		Triple Era 1st-year Epoch (San chi chia-tzu yuan li 三紀甲子元暦)	Chiang Chi 姜岌	384[-417]
14		11	19	N. Liang+		Epochal Beginning (Hsuan shih li 玄始暦)	Chao Fei 趙{匪+ r. side of 枚}	c. 412[-522] (note 2)
15			22	Sung		Seven Luminaries Past (Chi wang ch’i yao li 既往七曜暦)	Hsu Kuang 徐廣	c. 424
16			21	N. Wei		Triple Spreading Epoch (San hsuan yuan li 三宣元暦)	Ts’ui Hao 崔浩	c. 440
17	5	12	23, 24	Sung+	Epochal Excellence (Yuan chia li 元嘉暦)		Ho Ch’eng-t’ien 何承天	443-63 (note 3)
18	6	13	25	Sung	Great Enlightenment (Ta ming li 大明暦)		Tsu Ch’ung-chih 祖沖之	463-521 (note 4)
19			26	N. Wei		Luminous Enlightenment (Ching ming li 景明暦)	Kung-sun Ch’ung 公孫崇	507
20			27	N. Wei		Divine Tortoise (Shen kuei li 神龜暦)	Ts’ui Kuang 崔光	518? (note 5)
21	7	14	28	N. Wei	Orthodox Glory (Cheng kuang li 正光暦)		Chang Lung-hsiang 張龍祥	518-40
22			33	N. Ch’i		Numinous Pattern (Ling hsien li 靈憲暦)	Hsin-tu Fang 信都芳	by 539? (note 6)
23	8	15	29	E. Wei	Ascendant Harmony (Hsing ho li 興和暦)		Li Yeh-hsing 李業興	540-50
24		16	30	Liang		Great Unity (Ta t’ung li 大同暦)	Yü K’uo 虞	544
25		17	31	E. Wei		Nine-grid Chess (Chiu kung hsing ch’i li 九宮行棋暦)	Li Yeh-hsing	547 (note 7)
26	9	18	32	N. Ch’i	Celestial Preservation (T’ien pao li 天保暦)		Sung Ching-yeh 宋景業	550-66 (note 8)
27				N. Chou		Chou (Chou li 周暦? )	Ming K’o-jang 明克讓	559? (note 9)
28	10	19	34	N. Chou	Celestial Harmony (T’ien ho li天和暦)		Chen Luan 甄鸞	566-79
29		20	35	N. Ch’i		Martial Tranquillity (Wu p’ing li 武平暦)	Liu Hsiao-sun 劉孝孫	576
30		21	36	N. Ch’i		50th-year Epoch (Chia-yin yuan li 甲寅元暦)	Tung Chün 董峻	576
31		22	37	N. Ch’i		Meng-pin (Meng-pin li 孟賓暦)	Chang Meng-pin 張孟賓	576
32	11	23	38	N. Chou+	Great Emblem (Ta hsiang li大象暦)		Ma Hsien 馬顯	579-84
33	12	24	39	Sui	Opening Sovereignty (K’ai huang li開皇暦)		Chang Pin 張賓	584-608 (note 10)
34	42	25	40	Sui+	Sovereign Pole (Huang-chi li 皇極曆)		Liu Cho 劉焯	608
35	13	26	41	Sui	Great Patrimony (Ta yeh li大業暦)		Chang Chou-hsuan 張胄玄	608-19
36	14	27	42	T’ang	15th-Year (Wu-yin li 戊寅曆)		Fu Jen-chün傅仁均	619-65
37			45	T’ang		Warp and Weft (Ching-wei li 經緯暦)	Ch’ü-t’an Lo 瞿曇羅	by 664 (note 11)
38	15	29	44	T’ang	Chimera Virtue (Lin-te li麟德暦)		Li Ch’un-feng 李淳風	665-728
39			46	T’ang		Shining Residence (Kuang chai li 光宅暦)	Ch’ü-t’an Lo (Indian)	698
40		30	47	T’ang		Divine Dragon (Shen lung li 神龍暦)	Nan-kung Yueh 南宮說	705
41		28	48	T’ang		Nine Upholders (Chiu-chih li 九執暦)	Anonymous [Indian]	718 (note 12)
42	16	31	49	T’ang	Great Expansion (Ta-yen li 大衍暦		I-hsing 一行	728-62 (note 13)
43			50	T’ang		Thousand Year (Ch’ien sui li 千歲暦)	Wang Po 王勃	8th cent.
44			51	T’ang		Seven Luminaries (Ch’i yao li 七曜暦)	Wu Po-shan 吳伯善	8th cent.
45	17	32	53	T’ang	Fivefold Era (Wu chi li 五紀暦)		Kuo Hsien-chih 郭獻之	752-85 (note 14)
46			52	T’ang		Perfect Virtue (Chih te li 至德暦)	Han Ying 韓穎	758[-62]
47			43	T’ang		Tallying with Heaven (Fu t’ien li 符天暦)	Ts’ao Shih-wei 曹士蒍	780/83 (note 15)
48	18	33	54	T’ang	Constant Epoch (Chen yuan li貞元暦)	Constant Epoch (Cheng-yuan li 正元暦)	Hsu Ch'eng-ssu 徐承嗣	785-822 (note 16)
49			55	T’ang		Phenomenal Contemplation (Kuan hsiang li 觀象暦)	Hsu Ang 徐昂	807[-22] (note 17)
50	19	34	56	T’ang	Extending Enlightenment (Hsuan ming li 宣明暦)		Hsu Ang	822-93 (note 18)
51	20	35	57	T’ang+	Reverence for the Arcana (Ch’ung hsuan li 崇玄暦		Pien Kang 邊岡	893-956 (note 19)
52			59	F. Shu		Eternal Glory (Yung ch’ang li 永昌暦)	Hu Hsiu-lin 胡秀林	ca. 911?
53			60	F. Shu?		Correct Phenomena (Cheng hsiang li 正象暦)		after 911? (note 20)
54			58	5 Dyn.		Myriad Parts (Wan fen li 萬分暦)	Anonymous, popular	ca. 920?
55			61	L. Tsin		Adjusted Epoch (T’iao yuan li 調元暦)	Ma Ch’ung-chi 馬重績	938
56			62	S. T’ang		Centered and Upright (Zhong-zheng li 中正暦)	Ch’en Ch’eng-hsun 陳成勛	940
57			63	S. T’ang		Orderly Governance (Ch’i cheng li 齊政暦)	Unknown	940/75
58			64	L. Chou		Resplendent Arcana (Ming yuan li 明玄暦)	Wang Ch'u-no王處訥	956
59	21	36	65	L. Chou+	Veneration for Heaven (Ch’in t’ien li 欽天暦)		Wang P'u 王朴	956-60 (note 21)
60	22	37	66	Sung	Response to Heaven (Ying t’ien li 應天暦)		Wang Ch'u-no	960-81
61	23	38	67	Sung	Supernal Epoch (Ch’ien yuan li 乾元暦)		Wu Chao-su 吳昭素	981-1001
62			77	Liao		Great Enlightenment	Chia Chün 賈俊	994[-1126] (note 22)
63		39	68	Sung		Perfect Way (Chih tao li 至道理)	Wang Jui 王睿	995 (note 23)
64	24	40	69	Sung	Matching Heaven (I t’ien li 儀天暦)		Shih Hsu 史序	1001-24
65		41	70	Sung		Supernal Ascendance (Ch’ien hsing li 乾興暦)	Chang K’uei 張奎	1022
66	25	42	71	Sung	Reverence for Heaven (Ch’ung t’ien li 崇天暦)		Sung Hsing-ku 宋行古	1024-64
67	26	43	72	Sung	Resplendent Heaven (Ming t’ien li 明天暦)		Chou Ts’ung 周琮	1064-74
68	27	44	73	Sung	Oblatory Epoch (Feng yuan li 奉元暦)		Wei P'u 衛朴	1074-92 (note 24)
69	28	45	74	Sung	Contemplation of Heaven (Kuan t’ien li 觀天暦)		Huang Chü-ch'ing 皇居卿	1092-1103 (note 25)
70	29	46	75	Sung	Augury of Heaven (Chan t’ien li 占天暦)		Yao Shun-fu 姚舜輔	1103-6
71	30	47	76	Sung	Era Epoch (Chi yuan li 紀元暦)		Yao Shun-fu	1106-27
72	31	48	78	Chin	Great Enlightenment		Yang Chi 楊級	1127-80
73	33	49	79	Sung	Concordant Epoch (T’ung yuan li 統元暦)		Ch'en Te-i 陳得一	1135-67)
74	34	50	80	Sung	Supernal Way (Ch’ien tao li 乾道暦)		Liu Hsiao-jung 劉孝榮	1167-76 (note 26)
75	35	51	81	Sung	Splendor through Simplicity (Ch’un hsi li淳熙暦)		Liu Hsiao-jung	1176-91
76	32	53	82	Chin	Revised Great Enlightenment (Ch’ung hsiu Ta ming li 重修大明暦)		Chao Chih-wei 趙知微	1180-1281 (note 27)
77	43	52	83	Jin	Thirty-second Year (I wei li 乙未暦)		Yeh-lü Lü 耶律履	c. 1180
78		54	84	Sung		Repeated Five-star Conjunction (Wu-hsing tsai chü li 五行再聚暦)	Shih Wan 石萬	1187
79	36	55	85	Sung	Coincident Epoch (Hui yuan li 會元暦)		Liu Hsiao-jung	1191-99
80	37	56	86	Sung	Concord with Heaven (T’ung t’ien li 統天暦)		Yang Chung-fu 楊忠輔	1199-1207
81	38	57	87	Sung	Spreading Joy (K’ai hsi li開禧暦)		Pao Huan-chih 鮑澣之	1207-51
82		58	88	Yuan		Western Expedition 7th-year Epoch (Hsi cheng keng-wu yuan li 西征庚午元暦)	Yeh-lü Ch’u-ts’ai 耶律楚材	c. 1221 (note 28)
83	39	59	89	Sung	Protection through Simplicity (Ch’un yu li淳祐暦)		Li Te-ch'ing 李德卿	1250-52 (note 29)
84	40	60	90	Sung	Coincidence with Heaven (Hui t’ien li 會天暦)		T'an Yü 譚玉	1253-71
85			91	Yuan		Myriad Year (Wan nien li 萬年暦)	Jamāl al-Dīn (Persian)	1267
86	41	61	92	Sung	Attainment of Heaven (Ch’eng t’ien li 成天暦		Ch'en Ting 陳鼎	1271-76
87			93	Sung		Founded in Heaven (Pen t’ien li 本天暦)	Teng Kuang-chien 鄧廣薦	1276 (note 30)
88	44	62	94	Yuan	Season-Granting system (Shou shih li 授時暦)		Kuo Shou-ching 郭守敬	1281[-1384]
89		63	95	Ming	Muslim (Hui-hui li 回回暦)		Wu Po-tsung 吳伯宗	1382
90		64	96	Ming		Great Concordance 大統	Liu Chi 劉基	1384[-1644] (note 31)
91		65	97	Ming		Sagely Longevity Myriad Year (Sheng shou wan nien li 聖壽萬年暦)	Chu Tsai-yü 朱載堉	c. 1590? (note 32)
92		66	98	Ming		Yellow Bell (Huang chung li 黃鍾暦)	Chu Tsai-yü	by 1581
93-94		67-68		Ming		Titles unknown	Hsing Yun-lu 邢雲路	c. 1610 (note 33)
95		70	99	Ming		New Method (Hsin fa li 新法暦)	Hsu Kuang-ch’i 徐光啟	1628
96		71	101	Ch’ing		Temporal Pattern (Shih hsien li 時憲暦)	J. A. Schall v. Bell	1644[-1742]
97		69	100	Ch’ing		Hsiao-an (Hsiao-an li 曉庵暦)	Wang Hsi-shan 王錫闡	c. 1656 (n. 34)
98		72	102	Ch’ing		40th-year (Kuei-mao li 癸卯暦)	Ignatius Kögler	1742[-1644]

Notes

1. So far as we now understand it , the Grand Inception system of Pien Hsin et al. was a set of basic lunisolar procedures that Liu Hsin , ca. A.D. 1-5 , extended to include what became the standard contents of astronomical systems. See Sivin 1995a , chap. 2 , p. 11.

2. CMT 255 gives the title as Yuan shih li 元始暦. Early sources differ about the correct title of the regnal era for which the system is named. The difference is almost certainly due to a historical taboo, but Ch’en Yuan 1928 does not list a pertinent one.

3. When continued in use under the Ch’i dynasty, this system was renamed Established Epoch (Chien yuan 建元).

4. This outstanding system, because it was attacked by a court favorite, was not adopted in the Sung period, but it was used under the Liang and Ch’en dynasties. The dates of official use should be 510-89. See Sung shu, 13: 304-17.

5. Although Ts’ui proposed a system with this title, it was renamed Orthodox Glory when enacted in 518 (apparently not 521), although the source is slightly ambiguous. Li Yeh-hsing was the astronomer most prominently involved. See Wei shu, 107A: 2662-63.

6. This date is quite uncertain; see the discussion in Ch’en Mei-tung 2003: 294.

7. CMT gives the title as Chiu kung li 九宮暦, and CTK as Chiu kung hsing ta li 九宮行答暦. Chen Mei-tung corrects the error in 2003: 288-89.

8. The terminal date of use depends on when one ends the N. Ch’i dynasty. Although conservative historians end it in 557, with the beginning of the N. Chou period, the last year of its last ruler was 577. The year 566 is significant only as the date of the N. Chou’s second calendar reform (the first was very obscure), but this made it attractive to compilers seeking a hapless sequence.

9. See Yabuuti 1964: 455, item 12, and Ch’en Mei-tung 2003: 304-5.

10. The transition from this item to item 34 was actually in 609; see Sui shu, 17: 435.

11. On the dates of this and the next item, see Ch’en Mei-tung 2003: 357.

12. This is probably when this treatise was translated from Sanskrit or another Indian language. When it was compiled remains unknown (Ch’en 2003: 359). Yabuuti 1979 is a translation and study.

13. This system was replaced by the Perfect Virtue system in 758; see Hsin T’ang shu, 27B: 635.

14. This system was actually adopted in 763. See Hsin T’ang shu, 29: 695.

15. CTK lists only the epoch of this popular system (660), but it was compiled more than a century later; see Momo Hiroyuki 1964.

16. This system was official from 783 to 806. See Ch’en Mei-tung 2003: 401. The difference between the titles given in the Yuan system and by the two modern sources is due to a taboo on the personal name of the third Sung emperor (Ch’en Yuan 1928: 154).

17. See Hsin T’ang shu, 30A: 739.

18. This system was adopted in Korea from the early 9th century to 1392, and in Japan from 861 to 1684. In both countries the Season-granting system succeeded it; Ch’en Mei-tung 2003: 407.

19. CTK gives the title as Ch’ung yuan li 崇元暦, another instance of taboo avoidance.

20. CTK gives the epoch of this item as "Hou Shu Yen-k’ang yuan-nien後蜀延康元年," and that of the last as "Hou Shu Yung-p’ing yuan-nien," but basic reference works (e.g., Ku Ching 1995: 60, Li Ch’ung-chih 1981: 133) list the date of the latter as in Former Shu, and give no such reign as the former in the Five Dynasties. See also Ch’en Mei-tung 2003: 419.

21. Actually used until 963, when the Response to Heaven system superseded it. See Sung shih, 68: 1498.

22. For the dates, see Ch’en Mei-tung 2003: 491.

23. CTK unaccountably dates items 63-71 (its items 68-76) as Later Chou, but that dynasty ended in 960.

24. Actually used 1075-94, when the Contemplation of Heaven system replaced it; Yü hai, 10: 32a-33b.

25. Some early sources give the author’s name as Huang Chü-ch'ing 黃居卿; see Ch’en Mei-tung 2003: 485.

26. The transition from this item to the Splendor through Simplicity system came in 1177; Yü hai, 10: 35a-40b.

27. The Season-granting system lists this item out of chronological order, no doubt because it is a revision of item 72.

28. This pre-dynastic Yuan system is often cited (here by CMT) simply as Keng-wu yuan li. It survives in Yuan shih, ch. 57-58.

29. See my note to the Evaluation, s.v., for the correct dates, 1252-53.

30. For the date, see Yuan shih, 82: 1953.

31. Liu drafted this system in 1355, but it was not used until the Ming period; Ming shih, 31: 516-17.

32. On the dates of this and the next item, see the discussion in Ch’en Mei-tung 2003: 612.

33. CTK devotes its items 67-68 to lost treatises by Hsing Yun-lu. The excerpts in Ku chin lü li k’ao indicate that both are revisions of SGS. Of the remaining items in this table, 96 and the revision of it in 98 are treatises in the conventional mode. It is uncertain whether 95 and 97 were astronomical systems.

34. On this item see Sivin & Fang 1976: 1379-80.

Sources

CMT: Ch’en Mei-tung 陈美东. 1995. Ku li hsin t’an 古历新探 (New investigations of ancient astronomy). Shenyang: Liao-ning chiao-yü CPS. Essays from the 1980’s, which make up a systematic topical history of computational techniques and their evolving accuracy.

CTK: Ch’en Tsun-kuei 陈遵妫. 1980-84. Chung-kuo t’ien-wen-hsueh shih 中国天文学史 (History of Chinese astronomy). 3 vols. Shang-hai: Shang-hai Jen-min Ch'u-pan-she.

SGS: Shou-shih li 授時暦 (Season-Granting system). In Yuan shih 元史, "Li chih 暦志" (Treatise on mathematical astronomy, History of the Yuan dynasty), ch. 52-55.

Ch’en Mei-tung 陈美东. 2003. Chung-kuo k’o-hsueh chi-shu shih. T’ien-wen-hsueh chüan 中国科学技术史。天文学卷 (History of Chinese science and technology. Astronomy). Beijing: K’o-hsueh Ch’u-pan-she. Chronological and topical, much of it arranged by system. Covers to 1911. Indices of authors and writings.

Momo Hiroyuki 桃裕行. 1964. Futenreki ni tsuite 符天暦について (On the Tallying with Heaven astronomical system). Kagakushi kenkyū 科学史研究, 71: 118-19.

Sivin, Nathan. 1969. Cosmos and Computation in Early Chinese Mathematical Astronomy. Leiden: E. J. Brill. Reprinted in Sivin 1995a as chap. 2.

Sivin, Nathan; Fang Chaoying. 1976. Wang Hsi-shan. In Dictionary of Ming Biography. 1368-1644, ed. L. Carrington Goodrich, II, 1379-82. New York: Columbia University Press.

Sivin, Nathan. 1995a. Science in Ancient China. Researches and Reflections. Variorum Collected Studies Series. Aldershot, Hants: Variorum.

Ku chin lü li k’ao 古今律暦考 (Studies of mathematical harmonics and astronomy, ancient and modern). Hsing Yun-lu 邢雲路. 1607. In Pai pu ts’ung-shu chi-ch’eng 百部叢書集成.

Yü hai 玉海 (Ocean of jade [encyclopedia]). By Wang Ying-lin 王應麟. 1267?. Ed. of 1352, reprint, Taipei: Ta Hua Shu-chü, 1977.

Copyright reserved by Nathan Sivin. Please email
nsivin! at sas! dot upenn! dot edu! (but use normal form and omit the exclamation points)
with comments and corrections.

Back to Nathan Sivin's home page Back to the Department of History and Sociology of Science home page
Use your browser's "back" button to return to your last location.

Last Modified 2004.2.23.